A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.

Multiobjective evolutionary algorithms: A survey of the state of the art

Over the last three decades, a large number of evolutionary algorithms have been developed for solving multi-objective optimization problems. However, there lacks an upto-date and comprehensive software platform for researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve their real-world problems. The demand of such a common tool becomes even more urgent, when the source code of many proposed algorithms has not been made publicly available. To address these issues, we have developed a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes more than 50 multiobjective evolutionary algorithms and more than 100 multi-objective test problems, along with several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files. More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative experiments, embedding new algorithms, creating new test problems, and developing performance indicators. Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]

http://egon.cheme.cmu.edu/Papers/OaBB.pdf

An algorithmic framework for convex mixed integer nonlinear programs

Over the last three decades, a large number of evolutionary algorithms have been developed for solving multiobjective
optimization problems. However, there lacks an up-to-date and comprehensive software platform for
researchers to properly benchmark existing algorithms and for practitioners to apply selected algorithms to solve
their real-world problems. The demand of such a common tool becomes even more urgent, when the source code
of many proposed algorithms has not been made publicly available. To address these issues, we have developed
a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes
more than 50 multi-objective evolutionary algorithms and more than 100 multi-objective test problems, along with
several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users
to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files.
More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the
basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative
experiments, embedding new algorithms, creating new test problems, and developing performance indicators.
Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization

The recent development of efficient thermal prime movers for distributed generation is changing the focus of the production of electricity from large centralized power plants to local generation units scattered over the territory. The scientific community is addressing the analysis and planning of distributed energy resources with widespread approaches, taking into account technical, environmental, economic and social issues. The coupling of cogeneration systems to absorption/electric chillers or heat pumps, as well as the interactions with renewable sources, allow for setting up multi-generation systems for combined local production of different energy vectors such as electricity, heat (at different enthalpy levels), cooling power, hydrogen, various chemical substances, and so forth. Adoption of composite multi-generation systems may lead to significant benefits in terms of higher energy efficiency, reduced CO2 emissions, and enhanced economy. In this light, a key direction for improving the characteristics of the local energy production concerns the integration of the concepts of distributed energy resources and combined production of different energy vectors into a comprehensive distributed multi-generation (DMG) framework that entails various approaches to energy planning currently available in the literature. This paper outlines the main aspects of the DMG framework, illustrating its characteristics and summarizing the relevant DMG structures. The presentation is backed by an extended review of the most recent journal publications and reports.

Distributed multi-generation: A comprehensive view

http://users.abo.fi/twesterl/selected-publications/10.CACE-TW-FP-1995.pdf

An extended cutting plane method for solving convex MINLP problems

A genetic algorithms based multi-objective optimization technique was utilized in the training process of a feed forward neural network, using noisy data from an industrial iron blast furnace. The number of nodes in the hidden layer, the architecture of the lower part of the network, as well as the weights used in them were kept as variables, and a Pareto front was effectively constructed by minimizing the training error along with the network size. A predator-prey algorithm efficiently performed the optimization task and several important trends were observed.

A genetic algorithms based multi-objective neural net applied to noisy blast furnace data

Structural and operational optimisation of distributed energy systems

The processes in metallurgical industry are often extremely complex and measurements from their interior are scarce due to hostile conditions. Today's constraints on high productivity and minor impact on the environment still require that the processes be strictly controlled. Mathematical models can play a central role in achieving these goals. In cases where it is not possible, or economically feasible, to develop a mechanistic model of a process, an alternative is to use a data-driven approach, where a black-box model is built on historical process data. Feedforward neural networks have become popular nonlinear modeling tools for this purpose, but the selection of relevant inputs and appropriate network structure are still challenging tasks. The work presented in this paper tackles these problems in the development of a model of the blast furnace hot metal silicon content. A pruning algorithm is applied to find relevant inputs and their time lags, as well as an appropriate network connectivity, for solving the given time-series problem. In applying the model, an on-line learning of the upper-layer weights is proposed to adapt the model to changes in the input–output relations. The analysis shows results in good agreement with findings by other investigators and practical metallurgical knowledge.

https://www.jstage.jst.go.jp/article/isijinternational/47/12/47_12_1732/_pdf

Frank Pettersson

Papers

An extended cutting plane method for solving convex MINLP problems

A genetic algorithms based multi-objective neural net applied to noisy blast furnace data

Structural and operational optimisation of distributed energy systems

Nonlinear Prediction of the Hot Metal Silicon Content in the Blast Furnace

Hybrid ant colony optimization and visibility studies applied to a job-shop scheduling problem